Question

From the following data regarding the amount of rainfall (x) and the production of rice (y).

1. Find the most likely production corresponding to a rainfall of 50 cms.

2. Find the most likely rainfall corresponding to the production of 45 quintals.

| | Rainfall (cms) | Production (quintals) |
| Mean | 30 | 40 |
| Variance | 25 | 64 |

Coefficient of correlation = 0.6

Answer 1

Let x and y be the rainfall and production given:

x̄ = 30; ȳ = 40, = σ2x =25

∴ σx = 5 σ2y = 64

∴ σ2y =8; γ = 0.6

1. To find y when x = 50; we need the regression equation of y on x:

(y – ȳ) = byx (x – x̄)

1. To find x when y = 45, we need the regression equation of x on y: (x – x̄) = b × y (y – ȳ)

X = 1.875+ 30 = 31.875 cms rainfall.